Systems of Modular Equations

Question

Given the following systems of modular equations:

$$ 4^{x}+x^{2}\equiv 1 (mod \: 6)$$

$$7x\equiv 3 (mod \: 9)$$

$$15x\equiv 10 (mod \: 25)$$

Which x solves the system ?

It is possible to make use of Chinese remainder theorem, but what to do with Equation 1 ?

Thanks

Answer 1

Hint: The (positive) powers of $4$ are all congruent to $4$ mod $6$, so that first equation simplifies to

$$x^2\equiv3\mod6$$

Can you take it from there?